bug in isogenies

[chriswuthrich]

Something is wrong with the post_isomorphism of isogenies of elliptic curves :

sage: E = EllipticCurve(GF(17), [0,-1,0,-3,-1])
sage: P = E([16,0])
sage: phi = E.isogeny(P,codomain=E)
sage: phi(P)
(9 : 11 : 1)
sage: phi(P) in E
False

Component: elliptic curves

Keywords: isogeny

Author: Craig Citro, Chris Wuthrich

Reviewer: John Cremona

Merged: sage-4.3.4.alpha0

Issue created by migration from https://trac.sagemath.org/ticket/8349

[craigcitro]

Attachment: trac_8349.patch.gz

[craigcitro]

comment:1

Attached a quick fix -- I'm happy to let it be ignored if there's something classier to be done.

[chriswuthrich]

comment:2

Wow. That was very quick. But maybe a bit too quick.

sage: E = EllipticCurve('11a1')
sage: phi = E.isogeny(None,codomain=EllipticCurve('11a2'),degree=5)
sage: [phi(P) for P in E.torsion_points()]
[(0 : 1 : 0), (1/3 : 1/2 : 1), (1/3 : 1/2 : 1), (1/3 : 1/2 : 1), (1/3 : 1/2 : 1)]

again the images are not even on the codomain(). I.e. there is probably a second spot that needs a small change.

[chriswuthrich]

Attachment: trac_8349.2.patch.gz

[chriswuthrich]

comment:3

I think that should do it also for the kohel part.

[JohnCremona]

comment:4

What about lines 981, 1002, in the patched file? They both say

          return self.__E2(0)

so shouldn't they also be changed to return 0 on the correct codomain?

[chriswuthrich]

comment:5

No, these two lines must stay as they are. They do the right thing.

[JohnCremona]

comment:6

Replying to @categorie:

No, these two lines must stay as they are. They do the right thing.

OK, I trust you -- I tried to find an example where they did not do the right thing, and could not.

I'm happy -- patch (just the 2nd one) applies to 4.3.3 and test pass.

[JohnCremona]

Reviewer: John Cremona

[JohnCremona]

Author: Chris Wuthrich

[chriswuthrich]

Changed author from Chris Wuthrich to Craig Citro, Chris Wuthrich

[sagetrac-mvngu]

Merged: sage-4.3.4.alpha0

[sagetrac-mvngu]

comment:8

Merged trac_8349.2.patch.